Question

Three faces of a fair die are yellow, two faces are red and one face is blue. The die is tossed three times. The probability that the colours, yellow, red and blue, appear in the first, second and the third tosses respectively, is

• A. $\frac{1}{8}$
• B. $\frac{1}{27}$
• C. $\frac{1}{36}$
• D. $\frac{1}{216}$

Answer 1

The correct option is C $\frac{1}{36}$

According to given condition,
P (yellow at the first toss) $=\frac{3}{6}=\frac{1}{2}$
P (red at the second toss) $=\frac{2}{6}=\frac{1}{3}$
P (blue at the third toss) $=\frac{1}{6}$
All these events are independent. Therefore, the probability of the required event,
$P=\frac{1}{2}\times \frac{1}{3}\times \frac{1}{6}=\frac{1}{36}$